Cube Roots Of Unity

Let the cube root of 1 be x i.e., 3√ 1 = x.

Then by definition, x3 = 1 or x3 – 1 = 0 or (x – 1)
(x2 + x + 1) = 0

Either x – 1 = 0 i.e., x = 1 or (x2 + x + 1) = 0

Hence

Hence, there are three cube roots of unity which are which the first one is real and the other two are
conjugate complex numbers. These complex cube roots of unity are also called
imaginary cube roots of unity.

PROPERTIES OF THE CUBE ROOTS OF UNITY:

1. One imaginary cube root of unity is the square of the other.

Hence it is clear that one cube root of unity is the square of the other.

Hence if one imaginary cube root of unity be ω, then the other would be ω2.

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